Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Mathematical Analysis of the Coating Process Over a Porous Web Lubricated with Upper Convected Maxwell Fluid

Version 1 : Received: 12 May 2019 / Approved: 13 May 2019 / Online: 13 May 2019 (13:25:25 CEST)

A peer-reviewed article of this Preprint also exists.

Zafar, M.; A. Rana, M.; Zahid, M.; Ahmad, B. Mathematical Analysis of the Coating Process over a Porous Web Lubricated with Upper-Convected Maxwell Fluid. Coatings 2019, 9, 458. Zafar, M.; A. Rana, M.; Zahid, M.; Ahmad, B. Mathematical Analysis of the Coating Process over a Porous Web Lubricated with Upper-Convected Maxwell Fluid. Coatings 2019, 9, 458.

Journal reference: Coatings 2019, 9, 458
DOI: 10.3390/coatings9070458

## Abstract

Present study offers mathematical calculations of the roll-coating procedure lubricated with upper Convected Maxwell Fluid. An incompressible isothermal viscoelastic fluid is considered with roll and the porous web having uniform velocities. By employing Lubrication Approximation Theory, the desired equations of motion for the fluid concerned over porous web are modelled and analyzed. The suction rate on the web and injection rate at the roll surface are anticipated proportionate. Results for velocity profile and pressure gradient are obtained analytically. Fluid parameters of industrial significance i.e. detachment point, pressure, sheet /roll separating force, power contribution and coating thickness are also calculated numerically. Substantial and monotonic increase is witnessed in these quantities with the increase of flow parameters.

## Keywords

Convected Maxwell Flow; Roll Coating Analysis; Lubrication Approximation Theory; Numerical Procedures; Porous Web

## Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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